Does the integer K has a factor p such that : 1<p<k
So, basically it is asking whether "k" is prime or not ?


Statement 1:
K>4!

Insufficient : As for k=25, it is not prime, however for K=29, it is prime.


Statement 2:
13!+2 < K < 13!+13

Sufficient : As we know 13! is divisible by all the positive number less than 14.
Hence for all the numbers in the range (13!+2, 13!+13), we can find a divisor , for e.g. 13!+7 must be divisible by 7 since 7 already divides 13! completely..and so on..

Hence B.

Thanks

nice question!